Methods for generating spatially-clustered, support-attached nucleic acid amplicons include polony in situ PCR and emulsion PCR. In both cases, nucleic acid features as small as a micron can be produced, but both use limiting dilution to ensure clonal amplicons. This requirement limits the effective feature density per unit volume that can be achieved, as it is governed by Poisson statistics. Linear rolling circle amplification, multiple displacement amplification, and hyperbranched rolling circle amplification are all techniques which allow production of clonal amplicons without limiting dilution of template.